Abstract : Interaction of a small system S with a large reservoir R amounts to thermal relaxation of the reduced system density operator rho (t) subs. The presence of the reservoir enters the equation of motion for rho (t) subs through the reservoir correlation functions. Commonly, this time scale is much smaller than the inverse relaxation constants for the time evolution of rho (t) subs . Then a series of approximations can be made, which lead to a Markovian equation of motion. In this paper the assumption of a small reservoir correlation time is removed. The equation of motion for rho (t) subs is solved, and it appears that the memory effect, can be incorporated in a frequency dependence of the relaxation operator. Subsequently, (unequal-time) quantum correlation functions of two system operators are considered, where explicit expressions for (the Laplace transform of) the correlation functions are obtained. They involve again the relaxation operator which accounts for the time regression. Additionally, it is found that an initial-correlation functions do not factorized as rho (t) subs times the reservoir density operator. Keywords: Correlation functions; Reservoir theory; Finite memory time; Markov approximation; Correlation time; Relaxation constant.